Topological equivalence of complex polynomials

Details Topological equivalence of complex polynomials Topological equivalence of complex polynomials

2003-09-19

arxiv.org/abs/math/0309316v2

Adv. Math. 199 (2006), no.1, 136-150.

Mathematics

Algebraic Geometry

14 pages, revised text for final version

Scientific paper

10.1016/j.aim.2005.03.003

The following numerical control over the topological equivalence is proved: two complex polynomials in $n\not= 3$ variables and with isolated singularities are topologically equivalent if one deforms into the other by a continuous family of polynomial functions $f_s \colon \mathbb{C}^n \to \mathbb{C}$ with isolated singularities such that the degree, the number of vanishing cycles and the number of atypical values are constant in the family.

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